Stirling Numbers of Uniform Trees and Related Computational Experiments

Stirling Numbers and Generalized Zagreb Indices

We show how generalized Zagreb indices $M_1^k(G)$ can be computed by using a simple graph polynomial and Stirling numbers of the second kind. In that way we explain and clarify the meaning of a triangle of numbers used to establish the same result in an earlier reference.

Stirling Numbers and Records

A generalized recurrence formula for Stirling numbers and related sequences

In this note, we provide a combinatorial proof of a generalized recurrence formula satisfied by the Stirling numbers of the second kind. We obtain two extensions of this formula, one in terms of r-Whitney numbers and another in terms of q-Stirling numbers of Carlitz. Modifying our proof yields analogous formulas satisfied by the r-Stirling numbers of the first kind and by the r-Lah numbers.

Congruences on Stirling Numbers and Eulerian Numbers

In this paper, we establish some Fleck-Weisman type congruences for the Stirling numbers and the Eulerian numbers.

Log-concavity of Stirling Numbers and Unimodality of Stirling Distributions

A series of inequalities involving Stirling numbers of the first and second kinds with adjacent indices are obtained. Some of them show log-concavity of Stirling numbers in three different directions. The inequalities are used to prove unimodality or strong unimodality of all the subfamilies of Stirling probability functions. Some additional applications are also presented.